Simple harmonic motion of a spring and ball

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SUMMARY

The discussion centers on calculating the mass of a ball placed on two springs with spring constants of 575 N/m and 325 N/m. The ball compresses the first spring until it contacts the second spring, reaching an equilibrium position 12.5 cm above the table. The relevant equations for this problem include the period of oscillation formula, t=2π√(m/k), and the gravitational force equation, g=4π²l/T². The solution requires analyzing the forces acting on the ball at equilibrium, specifically the gravitational force and the forces exerted by both springs.

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  • Understanding of Hooke's Law and spring constants
  • Knowledge of simple harmonic motion principles
  • Familiarity with equilibrium conditions in physics
  • Basic algebra for solving equations
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  • Learn about the dynamics of simple harmonic motion and its equations
  • Explore equilibrium conditions and force balance in static systems
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Homework Statement


a ball that has been placed on top of a coil spring with a spring constant of 575 N/m and a length (h1) of 25.0 cm. As the ball compresses the spring, it contacts a second spring that has a spring constant of 325 N/m and a length (h2) of 15.0 cm. If the ball is 12.5 cm above the table when it reaches its equilibrium position, what is the mass of the ball?


Homework Equations


t=2pie√m/k, g= 4pie^2l/T^2


The Attempt at a Solution


would i add up the lengths, and add up the acclerations to find the total? in all the above formulas, i don't have enough variables to figure it out.
 
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You're making it too difficult - nothing is oscillating, so you don't have to solve a simple harmonic oscillator or find an acceleration. In fact, nothing is moving - at the end of the problem, everything is in equilibrium.

So, when everything is in equilibrium, the sum of all the forces must be equal to ... what?

What is the downward force on the mass due to gravity?
What is the upward force on the mass due to Spring 1?
What is the upward force on the mass due to Spring 2?
 

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